Washington (CNN)Sen. John McCain said Russian election-related hacks threaten to "destroy democracy" and faulted the American response as "totally paralyzed."

McCain, the Arizona Republican who chairs the Senate Armed Services Committee, again called for a select committee to investigate the CIA's finding that Russia hacked Democrats' emails in a bid to help President-elect Donald Trump defeat Hillary Clinton.

"This is the sign of a possible unraveling of the world order that was established after World War II, which has made one of the most peaceful periods in the history of the world," McCain told CNN's Jake Tapper on "State of the Union." "We're starting to see the strains and the unraveling of it, and that is because of the absolute failure of American leadership."

"When America doesn't lead, a lot of other bad people do," he added.

McCain's calls so far have been rejected by Senate Majority Leader Mitch McConnell and House Speaker Paul Ryan, who have backed investigations but said they want to see them conducted through already-existing Senate and House committees.

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"This is serious business. If they're able to harm the electoral process, they may destroy democracy, which is based on free and fair elections," he said.

McCain further ratcheted up pressure on McConnell Sunday, sending a letter to the majority leader asking him to allow for a Senate select committee to probe Russian hacking.

"Cyber is the rare kind of all-encompassing challenge for which the Congress's jurisdictional boundaries are an impediment to sufficient oversight and legislative action," McCain wrote to McConnell in a letter, cosigned by fellow GOP Sen. Lindsey Graham, incoming Senate Democratic Leader Chuck Schumer and Sen. Jack Reed, the top Democrat on the Senate Armed Services Committee.

"Only a select committee that is time-limited, cross-jurisdictional, and purpose-driven can address the challenge of cyber," wrote the bipartisan quartet of senators. "We believe it is justified by the extraordinary scope and scale of the cyber problem."

McCain told Tapper on "State of the Union" responsibility for cyber-security is spread too broadly today.

"The responsibilities for cyber is spread over about four different committees in the Senate, and each doing their own thing, frankly, is not going to be the most efficient way of arriving at a conclusion," he said.

In the interview, McCain spoke about the Russian hacking -- as well as China's seizure of a US underwater drone and the Syrian government's slaughter of the citizens of Aleppo -- in dire terms.

In making another call for a select committee to investigate Russian hacking, McCain mocked President Barack Obama's statement Friday that he had personally told Russian President Vladimir Putin to "cut it out."

"We need a select committee. We need to get to the bottom of this. We need to find out exactly what was done and what the implications of the attacks were, especially if they had an effect on our election," McCain said.

"There's no doubt they were interfering and no doubt it was a cyber-attack. The question now is how much and what damage and what should the United States of America do? And so far, we've been totally paralyzed," he said. "I'm sure that when Vladimir Putin was told quote 'cut it out' unquote, I'm sure that Vladimir Putin immediately stopped all cyber-activities. The truth is, they are hacking every single day."